When you think about how deeply Google is ingrained in the everyday culture of people across the planet and how its brand has become one of the most powerful names in the history of business, it's easy to forget that the company hasn't even been around for 15 years yet.

Despite its relatively recent arrival, Google has a preeminent place among the most important organizations on the planet. Sure, Apple and Microsoft make a lot more money than Google, and there are plenty of older companies and even governments that employ a lot more people, and service organizations like the Red Cross and the United Way that outwardly provide greater services to humanity. But, Google's primary mission "to organize the world‘s information and make it universally accessible and useful" is arguably the most important work of the early 21st century. A hundred years from now, when people look back at this period of time, that's likely to be the thing they point to as the biggest turning point of this era because of its ability to empower people economically, socially, intellectually, and politically.

On Monday, Google co-founder Larry Page took the reins of the company at a time when it has reached a crossroads. After being laser-focused on information search for its early history, the company has strayed in lots of different directions in recent years with many experiments that have largely ended in failure and a lot of head-scratching (e.g. Google Wave).

As Page takes over the CEO job from Eric Schmidt, who navigated the company through its coming of age, it's time for Google to refocus on what it wants to be now that it's all grown up. Here are the top two priorities that should be on Page's mind.

1. Get serious about product quality

Google became Google for two reasons: 1.) The quality of its search results were so much better than everyone else's, and 2.) The company refused to use display ads on Google.com and consequently rewrote the rules of Internet advertising. Let's put the second point aside for now, since Google isn't having any problems in the revenue department.

However, the quality of Google's search results are definitely under duress. Entire cottage industries and content farms have developed around gaming Google's algorithm in order to get their (often worthless) pages to the top of Google's search results. While Google fights a constant war with these "SEO spam" sites, it's not doing a very good job of keeping up. Experian Hitwise reported that Google's search success rate (users who visit a site after a search) dropped by 13% in 2010.

Even long-time Google and Web supporter Tim O'Reilly said, "It's clear that Google is losing some kind of war with the spammers. I think Google has in some ways taken their eye off the ball."

Page needs to devote more of Google's resources to fixing this problem and rally the troops around the idea of attacking this issue since it threatens to undermine everything that Google is trying to accomplish.

However, the quality problem isn't just an issue in search on Google.com. Google continues to release products into the market before those products are ready and let product problems languish for months or years before fixing them or simply pulling the plug on the product. For example, the first version of Android was a disaster when it was released in 2008 (a year later, the 2.0 version was finally acceptable). Google Apps had badly inconsistent features across its various office products for years after it was first released. And, products like Google Wave and Google Buzz were so badly conceived and poorly executed that they should have never been released to the public.

Page needs to rethink Google's product development and launch strategy and demand a much higher standard of quality before going to market. That doesn't mean Google should stop experimenting or running beta programs. Perish the thought. It just needs to get a lot more serious and discriminating about the way it launches products. And, it needs to devote more resources to search.

2. Forget Facebook

The worst thing Google can do right now is to get jealous about the media fawning over Facebook the way it used to fawn over Google. So what if magazines want to put Facebook's twentysomething CEO on their dead-tree leaflets. Google is 10 times more important than Facebook, which is rapidly devolving into a MySpace-like waste of digital bits.

Every few months there's a new rumor about Google launching its own social network to compete with Facebook — Google Me, Google Circles, etc. The best move Google could make in social is to not react to Facebook but simply play its own game. Continue to integrate social controls into search. Let the crowds help vote down the spam and worthless content in search. Allow people to connect to friends from their Google profile — if they choose — and allow friends' searching preferences, votes, and favorites to add a social filter to search results (and let the social filter be toggled on and off).

Google is already doing some of those things, but the point is that is the kind of stuff Google is really good at in the social space and that's the stuff it needs to focus on. On the other hand, building a social network does not play to Google's strengths. If you look at what the company created with Google Wave and Google Buzz, it's abundantly clear that this is not the kind of stuff Google engineers and product leaders should be spending their time doing.

If Google gets distracted chasing Facebook, it risks becoming like Microsoft, which has been so distracted chasing Google in the past five years that its core products have suffered considerably and are in greater danger than ever of losing their primacy.

Bottom line

Page needs to remember the mission that made Google great - organizing the world's information. He needs to re-energize the troops around that goal, launch an all-out assault on SEO spam, and keep from getting distracted by Facebook. The task of digitizing the world's data is far from complete — even just the public data. If Google can pull off more private-public partnerships like the one it's doing in Kansas City, Kansas for high speed fiber broadband than it can help also bring a lot more valuable information to the Web — from libraries to public documents to historical archives to government data, for example. This is a service for the Internet community and it enhances Google's business model by allowing people to use Google search for even more services.

As my colleague Larry Dignan noted, Google investors are going to be pressuring Page to find a big second revenue source beyond search. However, first Page will need to shore up Google's core mission and get the company refocused on the right product strategy. If he pulls it off, Google has a shot at solidifying its reputation for doing perhaps the most important work of the early 21st century.